问题
I want to linearly interpolate some metrics that are captured at times that fluctuate, to fixed timing intervals.
let original_times:[Double] = [0.0,1.3,2.2,3.4,4.2,5.5,6.6,7.2,8.4,9.5,10.0]
let metric_1:[Double] = [4,3,6,7,4,5,7,4,2,7,2]
let wanted_times:[Double] = [0,1,2,3,4,5,6,7,8,9,10]
//linearly resample metric_1 (with corresponding sampling times 'original_times') to fixed time interval times 'wanted_times'
Accelerate offers vDSP_vlint but I'm struggling to figure out how to implement it for my application.
func vDSP_vlint(_ __A: UnsafePointer<Float>, _ __B: UnsafePointer<Float>, _ __IB: vDSP_Stride, _ __C: UnsafeMutablePointer<Float>, _ __IC: vDSP_Stride, _ __N: vDSP_Length, _ __M: vDSP_Length)
回答1:
I don't understand the math you want to do 100%, but I do understand how to use Accelerate. I created a function which makes it easier to call this Accelerate function and shows you how it works.
/**
Vector linear interpolation between neighboring elements
- Parameter a: Input vector.
- Parameter b: Input vector: integer parts are indices into a and fractional parts are interpolation constants.
Performs the following operation:
```C
for (n = 0; n < N; ++n) {
double b = B[n];
double index = trunc([b]); //int part of B value
double alpha = b - index; //frac part of B value
double a0 = A[(int)index]; //indexed A value
double a1 = A[(int)index + 1]; //next A value
C[n] = a0 + (alpha * (a1 -a0)); //interpolated value
}
```
Generates vector C by interpolating between neighboring values of vector A as controlled by vector B. The integer portion of each element in B is the zero-based index of the first element of a pair of adjacent values in vector A.
The value of the corresponding element of C is derived from these two values by linear interpolation, using the fractional part of the value in B.
*/
func interpolate(inout a: [Double], inout b: [Double]) -> [Double] {
var c = [Double](count: b.count, repeatedValue: 0)
vDSP_vlintD(&a, &b, 1, &c, 1, UInt(b.count), UInt(a.count))
return c
}
EDIT: Alright, I wrapped my head around your problem, I understand now what you want to do. Was pretty fun to do, I came up with this:
import Accelerate
func calculateB(sampleTimes: [Double], outputTimes: [Double]) -> [Double] {
var i = 0
return outputTimes.map { (time: Double) -> Double in
defer {
if time > sampleTimes[i] { i++ }
}
return Double(i) + (time - sampleTimes[i]) / (sampleTimes[i+1] - sampleTimes[i])
}
}
func interpolate(inout b: [Double], inout data: [Double]) -> [Double] {
var c = [Double](count: b.count, repeatedValue: 0)
vDSP_vlintD(&data, &b, 1, &c, 1, UInt(b.count), UInt(data.count))
return c
}
let sampleTimes : [Double] = [0.0, 1.3, 2.2, 3.4, 4.2, 5.5, 6.6, 7.2, 8.4, 9.5, 10.0]
let outputTimes : [Double] = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
var metric_1 : [Double] = [4, 3, 6, 7, 4, 5, 7, 4, 2, 7, 2]
var metric_2 : [Double] = [5, 4, 7, 5, 6, 6, 1, 3, 1, 6, 7]
var metric_3 : [Double] = [9, 8, 5, 7, 4, 8, 5, 6, 8, 9, 5]
var b = calculateB(sampleTimes, outputTimes: outputTimes)
interpolate(&b, data: &metric_1) // [4, 3.230769, 5.333333, 6.666667, 4.75, 4.615385, 5.909091, 5, 2.666667, 4.727273, 2]
interpolate(&b, data: &metric_2) // [5, 4.230769, 6.333333, 5.666667, 5.75, 6, 3.727273, 2.333333, 1.666667, 3.727273, 7]
interpolate(&b, data: &metric_3) // [9, 8.230769, 5.666667, 6.333333, 4.75, 6.461538, 6.636364, 5.666667, 7.333333, 8.545455, 5]
The vars are necessary for Accelerate. I don't know how calculateB could be done with Accelerate, I mean it's possible I think, but it's a pain to search for the correct vDSP functions...
回答2:
Here's another solution without using any of the Accelerate stuff
public class Resampler {
///
/// ### Class method to resample some data
///
/// ### Inputs
/// - Actual time data that may not be regularly sampled
/// - Desired times you want the metric found at
/// - Metric data corresponding with actual time data
///
public class func resample( acualTimes atimes: [Double], desiredTimes dtimes: [Double], metric: [Double] ) ->[Double]
{
//
// Initialize the desired metrics array
//
var desiredMetrics: [Double] = [Double](count: dtimes.count, repeatedValue: 0);
// Initialize a counter to keep track of which metric value we are on
var counter: Int = 0;
// Loop through the desired times
for dtime in dtimes {
// Find the bounding indices, based on actual time data, for the desired time
// using a binary search
let (li, ri) = binarySearch(0,highBound: atimes.count-1, desiredTime: dtime, timeData: atimes);
// Find the desired metric using an interpolation
desiredMetrics[counter] = linearInterpolate(lowTime: atimes[li],
highTime: atimes[ri],
lowMetric: metric[li],
highMetric: metric[ri],
desiredTime: dtime);
// Increment the counter
counter++;
}
// Return the desired metrics
return desiredMetrics;
}
///
/// ### Binary search code to find the bounding time value indices
///
private class func binarySearch( lowBound: Int,
highBound: Int,
desiredTime: Double,
timeData: [Double]) -> (leftIndex: Int, rightIndex: Int)
{
if( highBound-lowBound == 1 ){
return (lowBound, highBound);
}else{
let center: Int = (lowBound + highBound)/2;
if( desiredTime <= timeData[center]){
return binarySearch(lowBound, highBound: center, desiredTime: desiredTime, timeData: timeData);
}else{
return binarySearch(center, highBound: highBound, desiredTime: desiredTime, timeData: timeData);
}
}
}
///
/// ### Linear interpolation method
///
private class func linearInterpolate( lowTime lt: Double,
highTime ht: Double,
lowMetric lm: Double,
highMetric hm: Double,
desiredTime dt: Double ) -> Double
{
return lm + (dt-lt)*(hm-lm)/(ht-lt);
}
}
And then you can run it by just doing the following:
let times: [Double] = [0.0,1.3,2.2,3.4,4.2,5.5,6.6,7.2,8.4,9.5,10.0];
let desiredTimes: [Double] = [0,1,2,3,4,5,6,7,8,9,10];
let metricData: [Double] = [4,3,6,7,4,5,7,4,2,7,2];
let desiredMetrics = Resampler.resample(acualTimes: times, desiredTimes: desiredTimes, metric: metricData);
print(desiredMetrics)
This example above will output:
[4.0, 3.23076923076923, 5.33333333333333, 6.66666666666667, 4.75, 4.61538461538461, 5.90909090909091, 5.0, 2.66666666666667, 4.72727272727273, 2.0]
回答3:
Another solution to the problem, 100% Accelerate:
import Accelerate
let metric_1: [Double] = [4.0, 3.0, 6.0, 7.0, 4.0, 5.0, 7.0, 4.0, 2.0, 7.0, 2.0]
let original_times: [Double] = [0.0, 1.3, 2.2, 3.4, 4.2, 5.5, 6.6, 7.2, 8.4, 9.5, 10.0]
let wanted_times: [Double] = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]
let count = metric_1.count
let length = vDSP_Length(count)
var output = [Double](repeating: 0, count: count)
var interpolationConstant = 2.0
// calculate interpolated times
vDSP_vintbD(original_times, 1, wanted_times, 1, &interpolationConstant, &output, 1, length)
// calculate interpolated values
vDSP_vlintD(metric_1, &output, 1, &output, 1, length, length)
output: [4.0,
3.2999999999999998,
5.3999999999999995,
6.5999999999999996,
4.6000000000000005,
4.5,
5.8000000000000007,
4.6000000000000005,
2.8000000000000007,
4.5,
2.0]
来源：https://stackoverflow.com/questions/32801059/linear-resampling-datapoints-captured-at-fluctuating-time-intervals-to-flxed-ti